Question

Find the ratio in which the line segment joining the points A(5,4,8) and B(6,2,1), is divided by XY plane​

Answer 1

Answer:

So, required ratio is 2:3 and line segment is divided externally.

Step-by-step explanation:

Let

P(4,8,10)

and

Q(6,10,-8)

are the given points and YZ plane divides the line segment joining these points in ratio

k:1

.<br> Coordinates of a point which divides the line internally in ratio

m:n

are given by<br>

((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n),(mz_2+nz_1)/(m+n))

<br> So,

R(x,y,z) = ((k(6)+1(4))/(k+1),(k(10)+1(8))/(k+1),(k(-8)+1(10))/(k+1))

<br>

=((6k+4)/(k+1),(10k+18)/(k+1),(-8k+10)/(k+1))

<br> As this is divided by YZ plane, x-coordinate will be

0

.<br>

:. (6k+4)/(k+1) = 0=> k = -2/3

<br> So, required ratio is

2:3

and line segment is divided externally